Classical Solutions of Hyperbolic Differential-Difference Equations

The paper studies the existence of classical solutions of two-dimensional hyperbolicequations in the half-plane and multidimensional hyperbolic equations in the half-space; theequations in question contain superpositions and sums of differential operators and translationoperators acting on the spatial variables that take all real values. Using integral transformationsfor all equations considered in the paper, multiparameter families of infinitely smooth solutionsare constructed in closed form, and sufficient conditions on the coefficients and translations in theequations are obtained that guarantee the existence of such solutions.